ON THE KNOTTED ELASTIC CURVES

According to the Bernoulli-Euler theory of elastic rods the bending energy of the wire is proportional to the total squared curvature of ${\gamma}$, which we will denote by $F({\gamma})=\int_{\gamma}k^2ds$. If the result of J.Langer and D.Singer [3] extend to knotted elastic curve, then we obtain the following. Let {${\gamma},M$} be a closed knotted elastic curve. If the curvature of ${\gamma}$ is nonzero for everywhere, then ${\gamma}$ lies on torus.